Euler-Euler two-phase flow simulation of tunnel erosion beneath marine pipelines

In this study an Euler-Euler two-phase model was developed to investigate the tunnel erosion beneath a submarine pipeline exposed to unidirectional flow. Both of the fluid and sediment phases were described via the Navier-Stokes equations, i.e. the model was implemented using time-averaged continuity and momentum equations for the fluid and sediment phases and a modified k−ε turbulence closure for the fluid phase. The fluid and sediment phases were coupled by considering the drag and lift interaction forces. The model was employed to simulate the tunnel erosion around the pipeline laid on an erodible bed. Comparison between the numerical result and experimental measurement confirms that the numerical model successfully predicts the bed profile and velocity field during the tunnel erosion. It is evident that the sediments are transported as the sheet-flow mode in the tunnel erosion stage. Also the transport rate under the pipe increases rapidly at the early stage and then reduces gradually at the end of the tunnel erosion beneath pipelines.     

Large Eddy Simulation for Plunge Breaker and Sediment Suspension

Breaking waves are a powerful agent for generating turbulence that plays an important role in many fluid dynamical processes, particularly in the mixing of materials. Breaking waves can dislodge sediment and throw it into suspension, which will then be carried by wave-induced steady current and tidal flow. In order to investigate sediment suspension by breaking waves, a numerical model based on large-eddy-simulation (LES) is developed. This numerical model can be used to simulate wave breaking and sediment suspension. The model consists of a free-surface model using the surface marker method combined with a two-dimensional model that solves the flow equations. The turbulence and the turbulent diffusion are described by a large-eddy-simulation (LES) method where the large turbulence features are simulated by solving the flow equations, and a subgrid model represents the small-scale turbulence that is not resolved by the flow model. A dynamic eddy viscosity subgrid scale stress model has been used for the     

分数阶Oldroyd-B黏弹性Poiseuille流的Laplace数值反演分析

采用Laplace数值反演的Stehfest算法研究了分数阶Oldroyd-B粘弹性流体在两平板间非定常的Poiseuille流动问题.首先,通过数值解与近似解析解的比较验证了Stehfest算法的有效性.其次,运用Stehfest算法对平板Poiseuille流动进行了研究,揭示了分数阶黏弹性平板流的速度过冲和应力过冲现象,指出这些现象对分数导数的阶数存在明显的依赖性.同时,数值结果表明,整数阶本构方程仅仅是分数阶本构方程的特例,分数阶本构方程较整数阶本构方程具有更广泛的适用性.     

Modelling ripple development under non-uniform flow and sediment supply-limited conditions in a laboratory flume

Results are reported herein of an open channel flow laboratory based study of the development of ripples on a fine silica sand bed, and under non-uniform turbulent subcritical flow conditions. The hydraulic model used included a diverging channel, which resulted in a variation of hydraulic and sediment transport parameters along the channel. Sediment supply limitation occurred during experimentation, impacting bed form development. The overall aim of this study was to improve the understanding and modelling capability of the development of bed forms under limited sediment supply and non-uniform flow conditions. In particular, the applicability of an existing empirical model capable of predicting ripple development was tested for the conditions of this study, using measured ripple dimensions. The ripple height and length results were extracted from detailed bed profile records, obtained using an acoustic Doppler probe traversed longitudinally over the sediment bed, at various experimentation time intervals. It was found that the non-uniform flow conditions affected the development rate of the bed forms, while sediment supply limitation impacted their steady state dimensions. The measured steady state ripple dimensions were lower, on average, than the corresponding equilibrium dimensions predicted using existing empirical equations. Non-uniform flow also caused the simultaneous occurrence of bed forms at different stages of development along the hydraulic model, where 3D and 2D ripples and incipient bed forms were recorded. Such a scenario can occur in estuarine and coastal flows, due to changing hydraulic conditions and/or a limitation of sediment supply. The ripple development model tested was verified for the conditions of this study, with its accuracy being shown to depend on an accurate determination of steady state parameters.     

Mathematical modeling of soil mixture flow surge and its application to coastal area

The purpose of this study is to investigate debris flow surge that is set up with a numerical model using governing equations applied by the dynamics of a liquid–solid mixture. This model is performed by applying the finite difference method to display elapses of time. To measure the behavior mechanisms of the debris flow surge, the following are analyzed: the flow discharge, flow depth, and sediment volume concentration at the end of downstream channel. The flow discharge and flow depth only surge right after the debris flow reaches the downstream channel as the berm width shortens. In contrast, as the berm width lengthens, the flow discharge and water flow recede. As the berm width decreases, the sediment concentration shows a high concentration and a great height difference at the inflection point. Vice versa, when the berm width increases, an inflection point can be seen, but it reveals a low concentration and a low height difference. The numerical model of this study was applied to the coast of South Korea and analyzed. This study will provide information in predicting disasters caused by debris flow and in planning for various counter measures to prevent disasters.     

潮流波浪联合输沙及海床冲淤演变的理论体系与其数学模拟

根据近岸带及河口区潮流、波浪、湍流各自物理尺度的不同,从Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和质量传输方程出发,利用Ｒｅｙｎｏｌｄｓ分解的方法,建立了模拟波浪 流联合输沙及海床冲淤演变的理论体系,给出了潮流作用下近岸波浪传播方程、波浪作用下潮流运动方程并通过利用波流合成底部切应力、底层湍流脉动随机特性,得出了波流联合作用下不平衡沙计算中泥沙起悬与沉降量的确定方法。本文模型应用于“广西合浦围垦工程潮流波浪     

往复流作用下海底管道局部冲刷机制数值模拟

基于开源的计算流体力学模式REEF3D,建立了海底管道局部冲刷水槽数值模型,在验证单向流实验结果的基础上,进一步对往复流作用下的海底管道局部冲刷机制进行了研究,并作对比分析。研究表明,总体上往复流对管道所在海床的局部冲刷规模比单向流弱。当流向改变后,原先下游的堆积区转变成上游,优先受到冲刷,并填充到管道下方的冲刷坑,同时使水流在管道下方的作用减弱。这种回填过程使短周期下的往复流作用需要更长的冲淤平衡时间。在回填与冲刷的共同作用下,上下游的冲刷坑坡度会因流向变化而变化。     

The influence of bend amplitude and planform morphology on flow and sedimentation in submarine channels

We present a series of experiments that investigate the morphology of sediment deposits within sinuous submarine channels of different sinuosity (S = 1.14–1.94) and planform (symmetric and asymmetric bends), generated by bedload-dominated turbidity current flows. Flows were generated by releasing dense saline gravity currents over a mobile sediment bed through pre-formed sinuous channels. Flows had a basal-outwards helicity and produced a characteristic bed morphology with point bars downstream of the bend apex at the inside of bends and scour at the outside of bends. An increasing loss of fluid through overspill with increasing channel sinuosity results in a decreasing magnitude of cross-stream velocity downstream, a decreasing amount of erosion and deposition, and decreasing transverse slopes of in-channel deposits. Basal fluid from within the channel is transported over the outer-levee at bends, implying that proximal outer-bend levee deposits will have similar sediment composition to that within the channel. More deposition of coarse material might be expected on levees and in overbank regions close to higher amplitude bends. No simple relationship was observed between superelevation and sinuosity, probably due to changes in the relative influences of downstream velocity and bend curvature on centrifugal force and inertial run-up. In the channel with the tightest initial bend curvature, overspill fluid from Bend 1 re-entered the channel at Bend 2, dominating flow characteristics and disrupting the basal-outwards helicity observed in the other channels. Higher sinuosity channels and those with shallow regional and levee slopes are thus more likely to have a higher proportion of anomalous flow and sedimentation patterns due to the influence of overspill fluid re-entry into the channel. The results of this investigation are combined with published observations to enable the synthesis of a new model for sedimentation in sinuous submarine channels.     

Numerical modeling of flow and scour below a pipeline in currents: Part II. Scour simulation

A vertical two-dimensional (2D) numerical model for time dependent local scour below offshore pipelines subject to unidirectional steady flow is developed. The governing equations for the flow and sediment transport are solved by using finite difference method in a general curvilinear coordinate system. The performance of two turbulence models, the standard k–ɛ model and Smagorinsky subgrid scale (SGS) model, on modeling time dependent scour processes is examined. Both suspended load and bed load are considered in the scour model. The suspended-load model is verified against two channel sediment transport cases. The change of bed level is calculated from the continuity equation of total sediment transport. A new time marching scheme and a sand slide scheme are proposed for the scour calculation. It is found that the proposed time marching scheme and sand slide model work well for both clear-water and live-bed scour situations and the standard k–ɛ turbulence closure is more preferable than the SGS model in the 2D scour model developed in this study.     

防潮闸启闭影响下的河口水流泥沙运动状态研究

为研究防潮闸启闭与跨水工程建设对河口地区水流泥沙运动状态的影响,以河口近闸跨水工程为背景,建立了以Godunov格式有限体积法为基础的二维浅水流动数学模型和基于固液二相流理论的二维水流泥沙数学模型,并以实测资料进行必要验证,结果较为吻合。在此基础上,建立了永定新河河口区域二维水沙数值模型,将该模型应用于滨海新区Z4线一期跨河工程段的水沙分析,并对工程建设后永定新河河口水流泥沙运动的变化趋势进行预报。结果表明永定新河河口二维全沙模型较为可靠,可为河口近闸跨水工程的相关分析提供研究思路和方法。     

一种新的海滩地下水和地表水耦合计算方法

海滩地下水与地表水之间的质量和动量交换对于近岸海域的泥沙输运、盐水入侵以及地表水与地下水中污染物质的迁移扩散有重要的影响。通过对描述地下水和地表水运动的控制方程的有限差分离散格式进行重新组织,构造了一种新的地下水和地表水的耦合计算方法。作为地表水与地下水的分界面的海滩动边界在该模型中可以被隐式的模拟,无需特别处理。通过与解析解和实验数据的比较,证明本文方法可以有效地对斜坡海滩的地下水和地表水运动进行模拟。     

A wave-resolving model for nearshore suspended sediment transport

This paper presents a wave-resolving sediment transport model, which is capable of simulating sediment suspension in the field-scale surf zone. The surf zone hydrodynamics is modeled by the non-hydrostatic model NHWAVE (Ma et al., 2012). The turbulent flow and suspended sediment are simulated in a coupled manner. Three effects of suspended sediment on turbulent flow field are considered: (1) baroclinic forcing effect; (2) turbulence damping effect and (3) bottom boundary layer effect. Through the validation with the laboratory measurements of suspended sediment under nonbreaking skewed waves and surfzone breaking waves, we demonstrate that the model can reasonably predict wave-averaged sediment profiles. The model is then utilized to simulate a rip current field experiment (RCEX) and nearshore suspended sediment transport. The offshore sediment transport by rip currents is captured by the model. The effects of suspended sediment on self-suspension are also investigated. The turbulence damping and bottom boundary layer effects are significant on sediment suspension. The suspended sediment creates a stably stratified water column, damping fluid turbulence and reducing turbulent diffusivity. The suspension of sediment also produces a stably stratified bottom boundary layer. Thus, the drag coefficient and bottom shear stress are reduced, causing less sediment pickup from the bottom. The cross-shore suspended sediment flux is analyzed as well. The mean Eulerian suspended sediment flux is shoreward outside the surf zone, while it is seaward in the surf zone.     

振荡流层移输沙条件下悬沙层泥沙扩散系数垂向分布特征研究

层移输沙是海岸带泥沙运动的主要形式之一,其垂向悬沙浓度分布规律的研究一直是海岸工程关心的重点。一般情况下,经典的纯扩散模型被用来描述和解释悬沙浓度的试验数据,该模型认为周期平均悬沙浓度主要由参考浓度、泥沙沉速和泥沙扩散系数确定。泥沙扩散系数可以由泥沙沉速和悬沙浓度的垂向梯度反演得到。既往研究大多直接给出泥沙扩散系数的结果,对于不同反演计算方法间结果差别的研究较少。本研究汇总了已有振荡流层移输沙试验数据,采用曲线拟合方法和直接差分方法计算了相应的泥沙扩散系数,研究表明两种方法得到的计算结果在垂向位置z 0.15 m处差异不大,随着垂向位置的升高,差分方法的计算结果略微大于拟合方法。考虑到拟合方法可以得到连续的泥沙扩散系数垂向分布,本研究推荐使用幂函数形式的曲线拟合方法求解悬移泥沙扩散系数。基于此,对比分析了层移输沙悬沙层泥沙扩散系数随泥沙粒径、振荡流周期、均方根流速和振荡流类型等物理参数的变化规律。在纯振荡流层移输沙条件下,泥沙扩散系数随泥沙粒径的增大而增大,而振荡流周期和均方根流速几乎不影响泥沙扩散系数。在振荡流和定常流共同作用下,泥沙扩散系数受振荡流周期和定常流流速的影响,泥沙扩散系数随着振荡流周期的增大或定常流流速的减小而增大。     

Incompressible SPH flow model for wave interactions with porous media

The paper presents an Incompressible Smoothed Particle Hydrodynamics (ISPH) method to simulate wave interactions with a porous medium. The SPH method is a mesh free particle modeling approach that is capable of tracking the large deformation of free surfaces in an easy and accurate manner. The ISPH method employs a strict incompressible hydrodynamic formulation to solve the fluid pressure and the numerical solution is obtained by using a two-step semi-implicit scheme. The ISPH flow model solves the unsteady 2D Navier–Stokes (NS) equations for the flows outside the porous media and the NS type model equations for the flows inside the porous media. The presence of porous media is considered by including additional friction forces into the equations. The developed ISPH model is first validated by the solitary and regular waves damping over a porous bed and the solitary wave interacting with a submerged porous breakwater. The convergence of the method and the sensitivity of relevant model parameters are discussed. Then the model is applied to the breaking wave interacting with a breakwater covered with a layer of porous materials. The computational results demonstrate that the ISPH flow model could provide a promising simulation tool in coastal hydrodynamic applications.     

Finite element analysis of flow control using porous media

A finite element model is established for simulating flow in and out a porous media. The extended Darcy equation inside the porous media and the Navier–Stokes equations in the fluid are coupled via the continuity condition at the interface between the two media. The model is firstly validated against the analytical and the numerical results available in literature. Then it is applied to simulate flow past a circular cylinder covered by a porous layer. The effect of the porous layer on the reduction of lift coefficient is investigated numerically. It is found that the lift reduction can be achieved by properly choosing the porous material. However, the amount of reduction greatly depends on the Reynolds number, the permeability and the Forchheimer coefficient.     

Intense near-bed sediment motions in waves and currents

In the past few years, two-phase models have been developed to describe the detail behaviour of fluid/sediment interactions and transport under the sheet flow conditions. Due to the complexity of the governing equations and uncertainties in the formulations of various stress terms, few complete solutions of these equations are known and the validations are thus far limited to only a few experimental data. In this paper, the numerical predictions of the behaviour of sheet flows using an improved version of an earlier two-phase flow model [Coastal Eng. 36(2) (1999) 87] are described. Although the general structure of the model was retained, a number of improvements had been made to give better account the underlying physics of the flow in areas very close to the stationary bed. All key flow parameters have been predicted and analysed in order to gain insight into the processes. Calculated time-dependent as well as time-averaged concentrations are compared with experimental data from purely oscillatory flows and oscillatory flow plus a current. Good qualitative agreements between predictions and measurements were achieved for the time-dependent concentrations while the time-averaged concentrations are quantitatively accurate as well.     

Numerical studies of gas hydrate systems: sensitivity to porosity-permeability models

The formation of sub-seafloor gas hydrates in marine environments can be described as a coupled transport and thermodynamic process inside a host sediment matrix undergoing structural evolution. The transport processes are driven by the sedimentary load and induced overpressure gradients, controlled by sediment permeability. In order to accurately model the resulting fluid flow profile, the decrease of sediment permeability during hydrate precipitation has to be taken into account, which affects both the transport of solutes and sediment compaction. In this paper, we investigate how total hydrate abundance is affected by regions of low permeability which deflect the flow field in their vicinity. For this purpose, a two-dimensional numerical hydrate system model was set up which permits to quantify this effect in scenarios where changes in water depth cause lateral variations of the thickness of the hydrate stability field, as well as of hydrate saturation and sediment permeability. The microscopic structure of gas hydrate crystals in the host sediment matrix defines the evolution of the permeability reduction during hydrate formation. Grain-coating precipitates have a stronger tendency to clog flow paths through pore throats than do pore-filling precipitates. Our results clearly show that these pore-scale processes affect the large-scale flow field and hydrate abundance. The sensitivity depends on the model geometry and, for a 5° slope of the seafloor, 4.1% relative difference is predicted for the hydrate saturation according to different porosity-permeability relationships.     

Fluid flow equations governing primary oil migration as a separate phase

A mathematical model of primary oil migration as a separate phase out of compacting shales is presented. During burial and oil generation, source rock porosity decreases and oil saturation increases until residual oil saturation is reached. At this stage oil is expelled out by capillary and excess fluid pressure gradients. The model is a system of differential equations which relate changes in oil and water saturation in time to water and oil flow out of the source rock during burial. An additional set of equations for periods of erosion of overburden are also provided. The equations can be numerically solved by finite difference method. If oil and water flow is to be simulated during oil generation, then at each time step, changes by oil generation in oil and water saturations and porosity must be calculated. The solution procedure is briefly outlined.